When beamforming a line array having uniformly spaced elements, grating lobes can appear if the element spacing exceeds one-half (½) of a wavelength. This effect is analogous to the aliasing that occurs when sampling time data at less than the Nyquist rate. In a narrowband sense, grating lobes introduce ambiguity. When wideband beamforming, these narrowband grating lobes smear out across bearing and raise the overall background level. This invention serves to cancel grating lobes, thus enabling operation of line arrays in a band above the ½ wavelength design frequency.
Referring to FIG. 1, a graph illustrating an exemplary beam pattern 100 associated with a line array having an under-sampled uniform element spacing, a spacing that exceeds half the wavelength associated with the design frequency of the array. As shown in FIG. 1, the beam pattern 100 comprises a main lobe 110 and an undesirable grating lobe 120. The occurrence of grating lobes such as grating lobe 120 is a well known problem in the art. Grating lobes are artifacts or a form of aliasing that result when a uniformly spaced array is operated above its half-wavelength design frequency.
Referring now to FIG. 2, graphs are shown that illustrate the problems encountered with grating lobes when broadband beamforming is carried out. Graph 200 illustrates the introduction of the grating lobe 210 as frequency increases. As can be seen in FIG. 2 the angle at which the grating lobe appears also varies as a function of frequency. Integration of this beam pattern 200 over frequency results in a broadband beam 250 with a smeared grating lobe 260 that appears as a background plateau. This smeared grating lobe 260 can mask desired signals.
Several approaches currently seek to address the grating lobe problem. The most basic approach simply involves raising the design frequency by decreasing channel-spacing over the entire array thereby raising sensor costs and processing requirements.
In another approach grating lobes are avoided by limiting the field of view and the operating frequency range. FIG. 3 illustrates beam patterns 310, 320 and 330 associated with three different steering angles of 90, 75 and 70 degrees respectively. The beam patterns 310 and 320 associated with 90 or 75 degrees shows minimal to no grating lobe interference, however when the main lobe is steered to 70 degrees a grating lobe 332 appears. The approach in this situation is simply to avoid steering beyond 70 degrees, which limits operational effectiveness in certain cases.
Referring now to FIGS. 4a and 4b, another approach for preventing grating lobes involves the use of an array with non-uniform element spacing. FIG. 4a illustrates a beam pattern 410 resulting from an array 420 with logarithmically-spaced array elements 430a-n. Grating lobe interference is avoided, however as can be higher side lobe levels are introduced.
Current methods for reducing grating lobe interference either require significant sensor hardware costs, merely attempt to avoid the problem, or introduce a host of additional problems. Improvements are thus needed to resolve these problems.